India's prime minister has appealed to the people of Indian-controlled Kashmir to end violent protests and said his government was ready to hold talks to resolve their long-standing problems.

"The years of violence should now end. Such violence will not benefit anyone," Manmohan Singh said in a speech marking India's Independence Day. "We are ready to talk to every person or group which abjures violence."

Indian-administered Kashmir has been rocked by near-daily protests and clashes with security forces, leading to the deaths of at least 57 people over the past two months. The protesters have set official buildings and vehicles ablaze and government forces have used guns and tear gas in an effort to contain the unrest.

Singh insisted that "Kashmir is an integral part of India", adding that "within this framework, we are ready to move forward in any talks".

At an independence day ceremony in Srinagar, the main city, a policeman in the audience in civilian clothes hurled a shoe at chief minister Omar Abdullah, the region's top elected official, and shouted: "We want freedom." The shoe missed its target, and Abdullah continued his speech after a pause. Authorities later said the policemen had been suspended from work in May and described him as mentally unstable.

Kashmir is divided between India and Pakistan but claimed by both. Anti-India sentiment runs deep in the portion of Kashmir it controls, with most people favouring independence from India or a merger with mostly Muslim Pakistan.

Singh said he had embarked on a new round of talks with political leaders from Kashmir last week and he wanted to take the process forward.

"India's democracy has the generosity and flexibility to be able to address the concerns of any area or group in the country," he said. In his 30-minute speech delivered from a bulletproof glass booth on the ramparts of a 17th-century fort in New Delhi, Singh referred to a host of other problems besetting India, including growing attacks by Maoist rebels and the need to speed up development programmes for millions of Indians still mired in poverty.

Singh also appealed to Maoist rebels, saying they should work with the government to speed up lagging economic development of rural areas, the main cause of the rebels' discontent. The rebels have tapped into the rural poor's growing anger at being left out of the country's economic gains. They now have a presence in 20 of India's 28 states.

Singh has often called the rebels the country's greatest internal security threat.

Referring to relations with neighbouring Pakistan, Singh said that Islamabad had to root out terrorist groups operating in its territory before peace talks between the nuclear-armed rivals can make any meaningful progress.

"If this is not done, we cannot progress far in our dialogue with Pakistan," he said.

Peace talks between India and Pakistan were stalled after the 2008 terror attack on Mumbai, India's financial hub, that killed 166 people. New Delhi blamed the attack on Lashkar-e-Taiba, a group Pakistan helped establish about 20 years ago to pressure India over Kashmir. Pakistan's government banned the group in 2002 following US pressure, but many analysts believe it still maintains links.

The US is eager for Pakistan and India to resolve their differences, in large part because it would free Pakistan to focus on the growing militancy along its border with Afghanistan.

In July the foreign ministers of India and Pakistan met in Islamabad in an effort to resume the dialogue that was in progress before the Mumbai attack.